identify the type of conic section that has the equation 16x^2+4y^2=16 and identify its domain and range.

Question

tkhunny · Answer

$ax^{2} + by^{2} = r^{2}$

$a > 0$
$b > 0$
Circle or Ellipse

$a = b$
Circle
$a\ne b$
Ellipse

This form is more visually obvious for Domain and Range:

$\dfrac{x^{2}}{1^{2}}+\dfrac{y^{2}}{2^{2}} = 1$, obtained with division by 16.

anonymous · Answer

so what is the domain and range?

tkhunny · Answer

You tell me.  I can't do all the work.

anonymous · Answer

i mean i dont really know how to work it out

tkhunny · Answer

Why have you been given this problem if you have no reasonable expectation of solving it?

Homework, these days!!  Very annoying.

Look under the x.  That $1^{2}$ suggests that the Domain reaches from -1 to +1 around the center of the ellipse.

Care to take a guess at what the $2^{2}$ under the y is telling us?

anonymous · Answer

the range from the two points?

tkhunny · Answer

The Range reaches from -2 to +2 around the center of the ellipse.

Since the center is (0,0) for this one, that makes Domain [-1,+1] and Range [-2,+2]

Do you have another one so I can see you do it?

anonymous · Answer

let me look if there is another one like this